Almost exact threshold calculations for covariance absolute value detection algorithm

Design of robust test statistics which mitigate the channel and noise uncertainties are the essential requirement of detection applications. Covariance absolute value (CAV) detection is one of the non-parametric detection methods which claims robustness [1]. Achieving the theoretical probability of detection performance depends on the accuracy in calculating the thresholding parameter, which in turn depends on the distribution of the test statistic under the null hypothesis. Since the exact analysis of distribution is cumbersome, approximation techniques are used. We present approximation techniques which achieve performance very close to the one obtained from exact distribution of the test statistic (using Monte-Carlo simulation). Further, an equivalent test statistic compared to CAV is proposed which uses the Bartlett decomposition of the sample covariance matrix and its performance is compared with CAV. The robustness of the proposed test statistic is verified for the noise uncertainty model assumed [2].